For all his faults, Tony Blair was an acute observer of the political scene. Surveying events from No 10, he would often muse that his party was fortunate that the Tories were badly served by supporters in the press: attempts to woo vital swing voters in the centre were constantly undermined by catcalls from the right.

Again, we see the truth of that analysis. Speak to people on the left, and they are spitting with rage at a government they perceive as comprised of heartless rightwing hardliners, slashing spending and savaging public services. Speak to those on the right, and they are angered by a government they see as run by soggy centrists held hostage by Liberal Democrats.

Clearly, mistakes have been made. The budget cut in the top rate of tax – demanded by the right – undermined six years of modernisation, and subsequent bungles reinforced the sense of a government losing touch with voters. But rows over pasties, fuel panics and even electronic snooping will not determine the next general election, although damage to the government's reputation for competence alarms party strategists. What really matters, as Blair knew so well, is relentless focus on the concerns of the centre.

This is so obvious it should not need stating. Swing voters in marginal seats win elections. The fact that it does demonstrates the danger of the Conservative party falling victim to the same fate that befell the Republicans, of tacking to the right to appease loudmouths. It is a recipe for electoral disaster.

This Tory version of the Tea Party movement calls for deeper cuts in public spending while urging tax cuts for the rich and opposing the removal of child benefit for high earners. Supporters claim to speak for ordinary people and seek tougher action on crime, on Europe, and on immigration – despite the lessons of the past, when banging on about such issues scared away moderate voters worried about jobs, schools and hospitals.

Now they oppose gay marriage and efforts to include ethnic minorities in the national debate, exemplified by harsh criticism of Tory chairman Sayeeda Warsi. "Just as the Tea Party attacks on Obama tip over into racism, so we see the same thing with Sayeeda," said one key insider. "It doesn't smell quite right, and wouldn't be happening if she were a white man."

The fury of this Tea Party tendency is puzzling, since the coalition is doing so many things they sought: reforming welfare, opening up the school system, forcing competition in the health service, tackling public-sector pensions and reducing the deficit. But it is never enough – just as with the militants who wrecked Labour in the 80s, and the zealots who made John Major's life a misery in the 90s. "Most parties go bonkers when out of power," said a Downing Street source. "Our base goes bonkers when we're in power."

Significantly, one prominent polemicist harked back to the Thatcher era this week, claiming that "wets" had recaptured the party after a brief hiatus. The Iron Lady's divisive shadow still hangs heavy over British politics. Indeed, it was no surprise to see Norman Tebbit, long an enemy of compassionate conservatism, so quick to attack (like a shark smelling blood in the water) when the government wobbled.

For all her achievements, Thatcher's legacy is why suspicion still shrouds the Tories – especially in key Midlands and north-west battlegrounds – and why the remoulding of the "nasty party" was incomplete at the last election. The right still claims the "big society" lost the election, an absurd argument when the party's lead in the polls dwindled after George Osborne embraced austerity. He was correct to do so, but for many voters it revived fears over the future of public services in Tory hands.

Yet still Tea Party types seek a return to their mythical golden age of Thatcher, ignoring the lessons of her pragmatism. So once again we hear tedious calls for a revival of grammar schools, forgetting that more closed under her tenure than at any other time. It is selection of teachers we need, not pupils.

The right should wake up and smell the coffee. Yes, Cameron's government needs to stop floundering and find a compelling narrative beyond cuts, but electoral realities make it hard to see the Tories winning an outright majority at the next election. Only one thing is certain: there would be no chance if they adopted the tactics of the Tea Party Tories.